The present invention relates to dividers, multipliers, Fourier Transformers and Convolvers and more particularly to the processing of electronic signals, for example analog and digital signals found in a computer. The Fourier transform (FT) and convolution (C) can now be computed optically or electronically. In optical processing, a first lens is used to obtain the FT and a second lens is used to obtain the C. This call all be seen in the Special Issue on Optical Computing of IEEE Proceedings January 1977 and particularly in the article therein by J. Goodman. In electronic processing, a Fourier or Fast Fourier transformer may be used to obtain the FT and a convolver, matched filter or correlator can be used to obtain the C. Fourier transformers and convolvers (which include matched filters and correlators) can be implemented as analog or digital devices, such as surface acoustic wave (SAW), charge coupled devices (CCD), shift registers (SR), random access memory (RAM), etc. This can all be seen in the Special Issue on Surface acoustic Wave Devices of IEEE Proceedings May 1976 and particularly in the articles therein by J. Maines and E. Paige and G. Kino, and in the book by L. Rabiner and B. Gold "Theory and Application of Digital Signal Processing" Prentice-Hall 1975.
In optical processing, each element of a transparency at the input or front focal plane of a first lens illuminates the lens along different length paths and the lens illuminates the output or back focal plane of the lens. Each element of the backplane of the lens receives a single ray of light from each element of the frontplane of the lens. It is the combination of illuminations from all elements of the input transparency in each element of the backplane of the lens that produces the FT in the backplane of the lens and thereby forming an optical Fourier transformer. In a similar manner, a first and second lens in series, with a front, middle and back focal planes and with transparencies in the front and middle planes, produces the C in the backplane of the second lens and thereby forming (one version of) an optical convolver. In other words, light rays can be spatially traced through optical lens systems to obtain the FT and C.
Electronic processors are based on general purpose (gp) and special purpose (sp) computers. Briefly gp computers implement the FT and C by writing algorithms in a software program while sp computers encode or build algorithms into the hardware. There is no tracing of spatial paths in gp electronic processors. In sp electronic processing, each element of a delay line at the input sends a signal along a different path to an adder at the output. Coefficient multipliers are used to multiply signals in each path and these are bulky, power consuming and slow acting devices. Often, multipliers are the most critical units of the processor. However, sp electronic processors are analogs of the optical lens in the sense that signals can be traced along different paths (including coefficient multipliers). For example, see FIG. 6.16 in the book by Rabiner and Gold.
However, there is no basic reason the spatial tracing of paths, inherent to the optical systems, cannot be implemented electronically without conventional multipliers and thereby to provide new and useful computational elements such as dividers, multipliers, Fourier transformers and convolvers. The ability to operate efficiently on 2-D data and to perform operations such as the FT and C are several advantages of the optical systems compared to the electronic ones. However, the outstanding feature of optical systems is the speed with which these parallel operations can be carried out. The outstanding deficiency of the optical systems is the inefficiency of spatial light modulators and demodulators (transducers) for coupling and decoupling electronic signals to light paths and this single area is presently limiting the lens based optical processor.
It is the purpose of the present invention to produce dividers, multipliers, sp electronic lenses, Fourier transformers and convolvers having the 2-D (two-dimensionality) and speed advantages of optical lens processors but without the disadvantage of coupling and decoupling electronic signals to optical lens paths and thereby capable of exceeding the practical capacity, speed and ease of access of present electronic systems by at least several orders of magnitude, at reduced size and cost.